The ability to spatially resolve the structure of objects may be helpful in understanding a number of physical systems and may provide insights into fields as diverse as astrophysics, molecular solvation dynamics, geophysical systems, the behavior of solid state materials, and biological systems. Likewise, temporal dynamics may be required for unraveling processes of physical systems in relation to internal and external stimuli. The capture of dynamic volumetric images from biological specimens may help unravel mysteries in diverse areas such as, for example, developmental biology, tumor growth, and tissue engineering.
Many biological processes are mediated chemically, and relevant mechanisms are often elucidated only by labeling these processes with fluorescent probes. Fluorescent imaging is pervasive in biological sciences owing to its molecular specificity, which allows for labeling of targeted processes. Current imaging techniques are limited in the speeds at which they can acquire 3D images of incoherent light (e.g., fluorescence). High speed 3D imaging of fluorescent light emission would be of great value in understanding biological dynamics by virtue of the ability to precisely label bio-chemicals of interest.
3D images formed from collection of incoherent light can be obtained with high spatial resolution using techniques that restrict illumination and/or detection to a small volume in the sample region. For example, high fidelity imaging of 3D fluorophore distributions is permitted by confocal and two-photon laser scanning microscopy (LSM). However, restricting data collection to a small volume may require serial data acquisition, which might limit imaging speed and/or may degrade the ability to track dynamic behavior in 3D. Although various techniques have been reported for improving the speed of data acquisition in LSM by multifocal techniques, parallelization of data acquisition is limited to the number of foci, imposing practical limitations on the update rate of such systems.
Conversely, illumination with a coherent radiation beam may allow for the possibility of exploiting diffraction to image the spatial organization of a specimen in a single shot, drastically increasing imaging speeds. Since the only requirements for obtaining such an image are recovery of the amplitude and phase of the diffracted coherent field, and adherence to the first Born or Rytov approximations, diffractive volumetric imaging can, in principle, span the electromagnetic spectrum. Volumetric imaging exploiting the physics of coherent wave diffraction, i.e., encoding propagation distance in the diffracted beam phase, has proven useful in seismic, ultrasonic and photo acoustic, optical, x-ray, and electron beam imaging systems for rapid detection of spatial organization and temporal dynamics. These techniques, generally referred to as coherent diffractive imaging (CDI), rely on the recording, or numerical recovery, of optical phase information that reveals the distance the light has travelled from the point at which it scatters in an object to where it is recorded with a detector. Reconstruction of a volumetric image is based on a model of propagation, possibly combined with a priori knowledge about the specimen.
Spatial phase information may not be directly detectable at optical frequencies, so interferometric techniques are conventionally used to extract the phase and amplitude of the diffracted signal field. Off axis holography is the most successful of these methods. In off axis holography a coherent reference beam bypasses the specimen and is made to interfere with light coherently scattered by the specimen from the illumination beam. In the lateral and axial dimensions, the coherent scattered beam accumulates a spatial phase of the form e[iπ(λΔz)−1(x−Δx)2] far from a scattering point, where Δz is the (axial) propagation distance and Δx is the lateral location. The resulting interference pattern is recorded with a detector array, e.g., a camera, and contains intensity modulations proportional to cos [1+π(λΔz)−1(x−Δx)2] that encode the phase difference between the two beams, ϕ=1+π(λΔz)−1(x−Δx)2. Phase information represents the location of coherent scattering locations in the object that are encoded as intensity modulations in the recorded image. With these methods, spatial phase recovery is only possible if coherence is maintained between object and reference optical fields. In digital holographic microscopy (DHM), the complex field (magnitude and phase) of the beam diffracted from the object is recovered and numerically refocused to the sample region, producing a volumetric representation of the object.
Alternatively, the amplitude and phase of a coherent field diffracted from an object can be recovered through inversion of coherent light propagation with a regularized, iterative optimization algorithm, negating the need to form an interference pattern. This type of imaging is often called lensless CDI, and a wide range of related techniques fall under this umbrella. These techniques have found widespread application in high-resolution imaging of nano scale objects, including biological specimens such as yeast and chromosomes. Until now the power of DHM and CDI has been largely inaccessible to fluorescent light emission due to the random phase of the emitted fluorescent light, which renders it incoherent. The lack of a deterministic phase relationship between emitters in the object rules out image reconstruction by spatial phase inversion. Because of the vast potential of increasing imaging speed, adaptation of coherent imaging techniques to incoherent light is a long-sought, yet elusive, goal in optical imaging. For example, methods for obtaining holograms with incoherent light have been studied since the early days of holography. Generally, these efforts attempted to project illumination structured with Fresnel zone plate (FZP) rings, or similar patterns, into a sample and then record the transmitted light. The spacing of the oscillations in the measured FZP rings is related to the propagation distance, thereby encoding depth information into the interference pattern. Adaptation of this method for fluorescently emitting objects has been implemented in optical scanning holography and fluorescence incoherent correlation holography.